# How do you find the equation of a parabola, vertex is (2,20) and the x-intercept (5,0)?

Jan 8, 2016

Since the problem provides the vertex, start with the vertex form equation for a parabola ...

#### Explanation:

$y = a {\left(x - h\right)}^{2} + k$

where, vertex $= \left(h , k\right)$

Using the data from the problem ...

$y = a {\left(x - 2\right)}^{2} + 20$

Next, solve for $a$ using the point (5,0) ...

$0 = a {\left(5 - 2\right)}^{2} + 20 = 9 a + 20$

$9 a = - 20$

$a = - \frac{20}{9}$

Finally, write the complete equation for the parabola ...

$y = \left(- \frac{20}{9}\right) {\left(x - 2\right)}^{2} + 20$

hope that helped